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May 2020 Checking for Prior-Data Conflict Using Prior-to-Posterior Divergences
David J. Nott, Xueou Wang, Michael Evans, Berthold-Georg Englert
Statist. Sci. 35(2): 234-253 (May 2020). DOI: 10.1214/19-STS731

Abstract

When using complex Bayesian models to combine information, checking consistency of the information contributed by different components of the model for inference is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models based on comparing the observed value of a prior-to-posterior divergence to its distribution under the prior predictive distribution for the data. The divergence measure used in our model check is a measure of how much beliefs have changed from prior to posterior, and can be thought of as a measure of the overall size of a relative belief function. It is shown that the proposed method is intuitive, has desirable properties, can be extended to hierarchical settings, and is related asymptotically to Jeffreys’ and reference prior distributions. In the case where calculations are difficult, the use of variational approximations as a way of relieving the computational burden is suggested. The methods are compared in a number of examples with an alternative but closely related approach in the literature based on the prior predictive distribution of a minimal sufficient statistic.

Citation

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David J. Nott. Xueou Wang. Michael Evans. Berthold-Georg Englert. "Checking for Prior-Data Conflict Using Prior-to-Posterior Divergences." Statist. Sci. 35 (2) 234 - 253, May 2020. https://doi.org/10.1214/19-STS731

Information

Published: May 2020
First available in Project Euclid: 3 June 2020

MathSciNet: MR4106603
Digital Object Identifier: 10.1214/19-STS731

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.35 • No. 2 • May 2020
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